Estimating health care costs at scale in low- and middle-income countries: Mathematical notations and frameworks for the application of cost functions.

Appropriate costing and economic modeling are major factors for the successful scale-up of health interventions. Various cost functions are currently being used to estimate costs of health interventions at scale in low- and middle-income countries (LMICs) potentially resulting in disparate cost projections. The aim of this study is to gain understanding of current methods used and provide guidance to inform the use of cost functions that is fit for purpose. We reviewed seven databases covering the economic and global health literature to identify studies reporting a quantitative analysis of costs informing the projected scale-up of a health intervention in LMICs between 2003 and 2019. Of the 8725 articles identified, 40 met the inclusion criteria. We classified studies according to the type of cost functions applied-accounting or econometric-and described the intended use of cost projections. Based on these findings, we developed new mathematical notations and cost function frameworks for the analysis of healthcare costs at scale in LMICs setting. These notations estimate variable returns to scale in cost projection methods, which is currently ignored in most studies. The frameworks help to balance simplicity versus accuracy and increase the overall transparency in reporting of methods.